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Titlebook: Néron Models; Siegfried Bosch,Werner Lütkebohmert,Michel Raynaud Book 1990 Springer-Verlag Berlin Heidelberg 1990 Abelsche Varietäten.Alge

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发表于 2025-3-21 19:08:17 | 显示全部楼层 |阅读模式
书目名称Néron Models
编辑Siegfried Bosch,Werner Lütkebohmert,Michel Raynaud
视频video
丛书名称Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathemati
图书封面Titlebook: Néron Models;  Siegfried Bosch,Werner Lütkebohmert,Michel Raynaud Book 1990 Springer-Verlag Berlin Heidelberg 1990 Abelsche Varietäten.Alge
描述Néron models were invented by A. Néron in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithmeticians and algebraic geometers have applied the theory of Néron models with great success. Quite recently, new developments in arithmetic algebraic geometry have prompted a desire to understand more about Néron models, and even to go back to the basics of their construction. The authors have taken this as their incentive to present a comprehensive treatment of Néron models. This volume of the renowned "Ergebnisse" series provides a detailed demonstration of the construction of Néron models from the point of view of Grothendieck‘s algebraic geometry. In the second part of the book the relationship between Néron models and the relative Picard functor in the case of Jacobian varieties is explained. The authors helpfully remind the reader of some important standard techniques of algebraic geometry. A special chapter surveys the theory of the Picard functor.
出版日期Book 1990
关键词Abelsche Varietäten; Algebra; Algebraische Gruppen; Arithmetic; Invariant; Jacobi-Varietäten; Picard-Funct
版次1
doihttps://doi.org/10.1007/978-3-642-51438-8
isbn_softcover978-3-642-08073-9
isbn_ebook978-3-642-51438-8Series ISSN 0071-1136 Series E-ISSN 2197-5655
issn_series 0071-1136
copyrightSpringer-Verlag Berlin Heidelberg 1990
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发表于 2025-3-21 21:30:24 | 显示全部楼层
https://doi.org/10.1007/978-3-642-51438-8Abelsche Varietäten; Algebra; Algebraische Gruppen; Arithmetic; Invariant; Jacobi-Varietäten; Picard-Funct
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978-3-642-08073-9Springer-Verlag Berlin Heidelberg 1990
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The Smoothening Process, assertion, we discuss the technique of blowing-up which is basic for obtaining smoothenings. The actual proof of the existence of smoothenings is carried out in Sections 3.3 and 3.4. As an application, we construct weak Néron models under appropriate conditions.
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From Birational Group Laws to Group Schemes,nlarged to a smooth .-group scheme; see 4.3/6. The purpose of the present section is to prove this result in the case where . is strictly henselian. In Chapter 6, the result will be extended to a more general base.
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,Néron Models of Not Necessarily Proper Algebraic Groups, dropping the condition that they are of finite type. Then, due to the smoothness, Néron lft-models are locally of finite type. This is the reason why we use the abbreviation “lft”. For example, tori do admit Néron lft-models whereas, for non-zero split tori, Néron models (in the original sense) do not exist.
发表于 2025-3-23 06:50:52 | 显示全部楼层
,What Is a Néron Model?,This chapter is meant to provide a first orientation to the basics of Néron models. Among other things, it contains an explanation of the context in which Néron models are considered, as well as a discussion of the main results on the construction and existence, including some examples.
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